- #1

fog37

- 1,568

- 108

A generic force ##F##, which may be conservative or not, performs mechanical work which is always equal to $$W=\Delta KE=KE_{final}-KE{initial}$$

i.e. produce a change in the object's kinetic energy ##KE##. Work is essentially a way to inject or subtract kinetic energy from a system.

If and only the force ##F## happens to be conservative, then we can define a new type of energy called potential energy ##PE##, such that the work done by ##F_{conservative}= -\Delta_{PE}= PE_{initial}-PE_{final}##.

This means that, for a conservative force, $$KE_{final}-KE_{initial} = PE_{initial}-PE_{final} $$ or equivalently $$PE_{initial}+KE_{initial} = PE_{final}+KE_{final} $$ $$ME_{initial} = ME_{final} $$ where ##ME = PE+KE##

So, it appears to me that the term "mechanical energy", since it encompasses potential energy, is only applicable to objects under the influence of conservative forces. Is that correct? If an object is only subject to nonconservative forces, it will only have kinetic energy and not potential energy. And if a system has potential energy, it has it only in virtue of the fact that conservative forces are acting on it, correct?

Conservative force can never be time-dependent which means that potential energy ##U(x,y,z)##is only a position-dependent quantity and is never time-dependent. If conservative forces were time-dependent, the mechanical energy of a system would not be conserved. What is the problem with having a time-varying mechanical energy? Is it not a useful concept? Is it just against the definition of conservative forces, i.e. forces that conserve mechanical energy?